LMFDB - Embedded newform 5290.2.a.bj.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5290,2,Mod(1,5290)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5290, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("5290.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5290 = 2 \cdot 5 \cdot 23^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5290.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$42.2408626693$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 3x^{9} - 15x^{8} + 35x^{7} + 78x^{6} - 123x^{5} - 185x^{4} + 140x^{3} + 177x^{2} - 15x - 23 $ x^10 - 3x^9 - 15x^8 + 35x^7 + 78x^6 - 123x^5 - 185x^4 + 140x^3 + 177x^2 - 15*x - 23
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 230)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$1.49412$ of defining polynomial
Character	$\chi$	$=$	5290.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -0.274376 q^{3} +1.00000 q^{4} +1.00000 q^{5} +0.274376 q^{6} +0.557477 q^{7} -1.00000 q^{8} -2.92472 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -0.274376 q^{3} +1.00000 q^{4} +1.00000 q^{5} +0.274376 q^{6} +0.557477 q^{7} -1.00000 q^{8} -2.92472 q^{9} -1.00000 q^{10} +5.07081 q^{11} -0.274376 q^{12} -4.07976 q^{13} -0.557477 q^{14} -0.274376 q^{15} +1.00000 q^{16} -0.583683 q^{17} +2.92472 q^{18} -0.242239 q^{19} +1.00000 q^{20} -0.152958 q^{21} -5.07081 q^{22} +0.274376 q^{24} +1.00000 q^{25} +4.07976 q^{26} +1.62560 q^{27} +0.557477 q^{28} +2.12655 q^{29} +0.274376 q^{30} -2.36730 q^{31} -1.00000 q^{32} -1.39131 q^{33} +0.583683 q^{34} +0.557477 q^{35} -2.92472 q^{36} +9.86429 q^{37} +0.242239 q^{38} +1.11939 q^{39} -1.00000 q^{40} -0.782659 q^{41} +0.152958 q^{42} +3.32343 q^{43} +5.07081 q^{44} -2.92472 q^{45} -11.3769 q^{47} -0.274376 q^{48} -6.68922 q^{49} -1.00000 q^{50} +0.160149 q^{51} -4.07976 q^{52} -1.66162 q^{53} -1.62560 q^{54} +5.07081 q^{55} -0.557477 q^{56} +0.0664646 q^{57} -2.12655 q^{58} -1.87547 q^{59} -0.274376 q^{60} +13.3689 q^{61} +2.36730 q^{62} -1.63046 q^{63} +1.00000 q^{64} -4.07976 q^{65} +1.39131 q^{66} -6.18087 q^{67} -0.583683 q^{68} -0.557477 q^{70} +2.92096 q^{71} +2.92472 q^{72} +7.94647 q^{73} -9.86429 q^{74} -0.274376 q^{75} -0.242239 q^{76} +2.82686 q^{77} -1.11939 q^{78} +13.7473 q^{79} +1.00000 q^{80} +8.32813 q^{81} +0.782659 q^{82} +3.81224 q^{83} -0.152958 q^{84} -0.583683 q^{85} -3.32343 q^{86} -0.583475 q^{87} -5.07081 q^{88} +15.5397 q^{89} +2.92472 q^{90} -2.27437 q^{91} +0.649529 q^{93} +11.3769 q^{94} -0.242239 q^{95} +0.274376 q^{96} -8.24519 q^{97} +6.68922 q^{98} -14.8307 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 10 q^{2} + 4 q^{3} + 10 q^{4} + 10 q^{5} - 4 q^{6} - 7 q^{7} - 10 q^{8} + 14 q^{9}+O(q^{10}) $ 10 * q - 10 * q^2 + 4 * q^3 + 10 * q^4 + 10 * q^5 - 4 * q^6 - 7 * q^7 - 10 * q^8 + 14 * q^9	\( 10 q - 10 q^{2} + 4 q^{3} + 10 q^{4} + 10 q^{5} - 4 q^{6} - 7 q^{7} - 10 q^{8} + 14 q^{9} - 10 q^{10} + 9 q^{11} + 4 q^{12} - 7 q^{13} + 7 q^{14} + 4 q^{15} + 10 q^{16} - 18 q^{17} - 14 q^{18} + 16 q^{19} + 10 q^{20} + 12 q^{21} - 9 q^{22} - 4 q^{24} + 10 q^{25} + 7 q^{26} + 13 q^{27} - 7 q^{28} + 10 q^{29} - 4 q^{30} - 3 q^{31} - 10 q^{32} + 25 q^{33} + 18 q^{34} - 7 q^{35} + 14 q^{36} - 8 q^{37} - 16 q^{38} + 12 q^{39} - 10 q^{40} + 10 q^{41} - 12 q^{42} - 9 q^{43} + 9 q^{44} + 14 q^{45} + 21 q^{47} + 4 q^{48} + 7 q^{49} - 10 q^{50} - 9 q^{51} - 7 q^{52} - 40 q^{53} - 13 q^{54} + 9 q^{55} + 7 q^{56} + 9 q^{57} - 10 q^{58} + 29 q^{59} + 4 q^{60} + 25 q^{61} + 3 q^{62} + 6 q^{63} + 10 q^{64} - 7 q^{65} - 25 q^{66} - 7 q^{67} - 18 q^{68} + 7 q^{70} + 64 q^{71} - 14 q^{72} - 16 q^{73} + 8 q^{74} + 4 q^{75} + 16 q^{76} + 57 q^{77} - 12 q^{78} + 44 q^{79} + 10 q^{80} + 14 q^{81} - 10 q^{82} - 26 q^{83} + 12 q^{84} - 18 q^{85} + 9 q^{86} + 25 q^{87} - 9 q^{88} + 11 q^{89} - 14 q^{90} + 5 q^{93} - 21 q^{94} + 16 q^{95} - 4 q^{96} - 10 q^{97} - 7 q^{98} + 13 q^{99}+O(q^{100}) \) 10 * q - 10 * q^2 + 4 * q^3 + 10 * q^4 + 10 * q^5 - 4 * q^6 - 7 * q^7 - 10 * q^8 + 14 * q^9 - 10 * q^10 + 9 * q^11 + 4 * q^12 - 7 * q^13 + 7 * q^14 + 4 * q^15 + 10 * q^16 - 18 * q^17 - 14 * q^18 + 16 * q^19 + 10 * q^20 + 12 * q^21 - 9 * q^22 - 4 * q^24 + 10 * q^25 + 7 * q^26 + 13 * q^27 - 7 * q^28 + 10 * q^29 - 4 * q^30 - 3 * q^31 - 10 * q^32 + 25 * q^33 + 18 * q^34 - 7 * q^35 + 14 * q^36 - 8 * q^37 - 16 * q^38 + 12 * q^39 - 10 * q^40 + 10 * q^41 - 12 * q^42 - 9 * q^43 + 9 * q^44 + 14 * q^45 + 21 * q^47 + 4 * q^48 + 7 * q^49 - 10 * q^50 - 9 * q^51 - 7 * q^52 - 40 * q^53 - 13 * q^54 + 9 * q^55 + 7 * q^56 + 9 * q^57 - 10 * q^58 + 29 * q^59 + 4 * q^60 + 25 * q^61 + 3 * q^62 + 6 * q^63 + 10 * q^64 - 7 * q^65 - 25 * q^66 - 7 * q^67 - 18 * q^68 + 7 * q^70 + 64 * q^71 - 14 * q^72 - 16 * q^73 + 8 * q^74 + 4 * q^75 + 16 * q^76 + 57 * q^77 - 12 * q^78 + 44 * q^79 + 10 * q^80 + 14 * q^81 - 10 * q^82 - 26 * q^83 + 12 * q^84 - 18 * q^85 + 9 * q^86 + 25 * q^87 - 9 * q^88 + 11 * q^89 - 14 * q^90 + 5 * q^93 - 21 * q^94 + 16 * q^95 - 4 * q^96 - 10 * q^97 - 7 * q^98 + 13 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−0.274376	−0.158411	−0.0792055	−	0.996858i	$-0.525238\pi$
$3$	−0.274376	−0.158411	−0.0792055	+	0.996858i	$0.525238\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0.274376	0.112014
$7$	0.557477	0.210706	0.105353	−	0.994435i	$-0.466403\pi$
$7$	0.557477	0.210706	0.105353	+	0.994435i	$0.466403\pi$
$8$	−1.00000	−0.353553
$9$	−2.92472	−0.974906
$10$	−1.00000	−0.316228
$11$	5.07081	1.52891	0.764454	−	0.644678i	$-0.223009\pi$
$11$	5.07081	1.52891	0.764454	+	0.644678i	$0.223009\pi$
$12$	−0.274376	−0.0792055
$13$	−4.07976	−1.13152	−0.565761	−	0.824569i	$-0.691418\pi$
$13$	−4.07976	−1.13152	−0.565761	+	0.824569i	$0.691418\pi$
$14$	−0.557477	−0.148992
$15$	−0.274376	−0.0708436
$16$	1.00000	0.250000
$17$	−0.583683	−0.141564	−0.0707819	−	0.997492i	$-0.522549\pi$
$17$	−0.583683	−0.141564	−0.0707819	+	0.997492i	$0.522549\pi$
$18$	2.92472	0.689363
$19$	−0.242239	−0.0555734	−0.0277867	−	0.999614i	$-0.508846\pi$
$19$	−0.242239	−0.0555734	−0.0277867	+	0.999614i	$0.508846\pi$
$20$	1.00000	0.223607
$21$	−0.152958	−0.0333782
$22$	−5.07081	−1.08110
$23$	0	0
$23$	0	0
$24$	0.274376	0.0560068
$25$	1.00000	0.200000
$26$	4.07976	0.800107
$27$	1.62560	0.312847
$28$	0.557477	0.105353
$29$	2.12655	0.394891	0.197445	−	0.980314i	$-0.436736\pi$
$29$	2.12655	0.394891	0.197445	+	0.980314i	$0.436736\pi$
$30$	0.274376	0.0500940
$31$	−2.36730	−0.425179	−0.212589	−	0.977142i	$-0.568190\pi$
$31$	−2.36730	−0.425179	−0.212589	+	0.977142i	$0.568190\pi$
$32$	−1.00000	−0.176777
$33$	−1.39131	−0.242196
$34$	0.583683	0.100101
$35$	0.557477	0.0942308
$36$	−2.92472	−0.487453
$37$	9.86429	1.62168	0.810840	−	0.585268i	$-0.199011\pi$
$37$	9.86429	1.62168	0.810840	+	0.585268i	$0.199011\pi$
$38$	0.242239	0.0392964
$39$	1.11939	0.179246
$40$	−1.00000	−0.158114
$41$	−0.782659	−0.122231	−0.0611154	−	0.998131i	$-0.519466\pi$
$41$	−0.782659	−0.122231	−0.0611154	+	0.998131i	$0.519466\pi$
$42$	0.152958	0.0236020
$43$	3.32343	0.506819	0.253409	−	0.967359i	$-0.418448\pi$
$43$	3.32343	0.506819	0.253409	+	0.967359i	$0.418448\pi$
$44$	5.07081	0.764454
$45$	−2.92472	−0.435991
$46$	0	0
$47$	−11.3769	−1.65950	−0.829749	−	0.558136i	$-0.811517\pi$
$47$	−11.3769	−1.65950	−0.829749	+	0.558136i	$0.811517\pi$
$48$	−0.274376	−0.0396028
$49$	−6.68922	−0.955603
$50$	−1.00000	−0.141421
$51$	0.160149	0.0224253
$52$	−4.07976	−0.565761
$53$	−1.66162	−0.228241	−0.114120	−	0.993467i	$-0.536405\pi$
$53$	−1.66162	−0.228241	−0.114120	+	0.993467i	$0.536405\pi$
$54$	−1.62560	−0.221216
$55$	5.07081	0.683748
$56$	−0.557477	−0.0744960
$57$	0.0664646	0.00880345
$58$	−2.12655	−0.279230
$59$	−1.87547	−0.244165	−0.122083	−	0.992520i	$-0.538957\pi$
$59$	−1.87547	−0.244165	−0.122083	+	0.992520i	$0.538957\pi$
$60$	−0.274376	−0.0354218
$61$	13.3689	1.71171	0.855854	−	0.517218i	$-0.173032\pi$
$61$	13.3689	1.71171	0.855854	+	0.517218i	$0.173032\pi$
$62$	2.36730	0.300647
$63$	−1.63046	−0.205419
$64$	1.00000	0.125000
$65$	−4.07976	−0.506032
$66$	1.39131	0.171258
$67$	−6.18087	−0.755113	−0.377556	−	0.925987i	$-0.623236\pi$
$67$	−6.18087	−0.755113	−0.377556	+	0.925987i	$0.623236\pi$
$68$	−0.583683	−0.0707819
$69$	0	0
$70$	−0.557477	−0.0666312
$71$	2.92096	0.346654	0.173327	−	0.984864i	$-0.444548\pi$
$71$	2.92096	0.346654	0.173327	+	0.984864i	$0.444548\pi$
$72$	2.92472	0.344681
$73$	7.94647	0.930064	0.465032	−	0.885294i	$-0.346043\pi$
$73$	7.94647	0.930064	0.465032	+	0.885294i	$0.346043\pi$
$74$	−9.86429	−1.14670
$75$	−0.274376	−0.0316822
$76$	−0.242239	−0.0277867
$77$	2.82686	0.322151
$78$	−1.11939	−0.126746
$79$	13.7473	1.54669	0.773346	−	0.633985i	$-0.218582\pi$
$79$	13.7473	1.54669	0.773346	+	0.633985i	$0.218582\pi$
$80$	1.00000	0.111803
$81$	8.32813	0.925348
$82$	0.782659	0.0864302
$83$	3.81224	0.418448	0.209224	−	0.977868i	$-0.432906\pi$
$83$	3.81224	0.418448	0.209224	+	0.977868i	$0.432906\pi$
$84$	−0.152958	−0.0166891
$85$	−0.583683	−0.0633093
$86$	−3.32343	−0.358375
$87$	−0.583475	−0.0625550
$88$	−5.07081	−0.540551
$89$	15.5397	1.64720	0.823602	−	0.567169i	$-0.191961\pi$
$89$	15.5397	1.64720	0.823602	+	0.567169i	$0.191961\pi$
$90$	2.92472	0.308292
$91$	−2.27437	−0.238419
$92$	0	0
$93$	0.649529	0.0673530
$94$	11.3769	1.17344
$95$	−0.242239	−0.0248532
$96$	0.274376	0.0280034
$97$	−8.24519	−0.837172	−0.418586	−	0.908177i	$-0.637474\pi$
$97$	−8.24519	−0.837172	−0.418586	+	0.908177i	$0.637474\pi$
$98$	6.68922	0.675713
$99$	−14.8307	−1.49054
$100$	1.00000	0.100000
$101$	9.47663	0.942960	0.471480	−	0.881877i	$-0.343720\pi$
$101$	9.47663	0.942960	0.471480	+	0.881877i	$0.343720\pi$
$102$	−0.160149	−0.0158571
$103$	9.38768	0.924995	0.462498	−	0.886620i	$-0.346953\pi$
$103$	9.38768	0.924995	0.462498	+	0.886620i	$0.346953\pi$
$104$	4.07976	0.400053
$105$	−0.152958	−0.0149272
$106$	1.66162	0.161391
$107$	−15.0177	−1.45181	−0.725907	−	0.687792i	$-0.758580\pi$
$107$	−15.0177	−1.45181	−0.725907	+	0.687792i	$0.758580\pi$
$108$	1.62560	0.156423
$109$	−13.1767	−1.26210	−0.631051	−	0.775741i	$-0.717376\pi$
$109$	−13.1767	−1.26210	−0.631051	+	0.775741i	$0.717376\pi$
$110$	−5.07081	−0.483483
$111$	−2.70653	−0.256892
$112$	0.557477	0.0526766
$113$	6.95642	0.654405	0.327203	−	0.944954i	$-0.393894\pi$
$113$	6.95642	0.654405	0.327203	+	0.944954i	$0.393894\pi$
$114$	−0.0664646	−0.00622498
$115$	0	0
$116$	2.12655	0.197445
$117$	11.9321	1.10313
$118$	1.87547	0.172651
$119$	−0.325390	−0.0298284
$120$	0.274376	0.0250470
$121$	14.7132	1.33756
$122$	−13.3689	−1.21036
$123$	0.214743	0.0193627
$124$	−2.36730	−0.212589
$125$	1.00000	0.0894427
$126$	1.63046	0.145253
$127$	10.0296	0.889985	0.444992	−	0.895534i	$-0.353206\pi$
$127$	10.0296	0.889985	0.444992	+	0.895534i	$0.353206\pi$
$128$	−1.00000	−0.0883883
$129$	−0.911870	−0.0802857
$130$	4.07976	0.357819
$131$	16.5560	1.44650	0.723250	−	0.690586i	$-0.242647\pi$
$131$	16.5560	1.44650	0.723250	+	0.690586i	$0.242647\pi$
$132$	−1.39131	−0.121098
$133$	−0.135043	−0.0117097
$134$	6.18087	0.533945
$135$	1.62560	0.139909
$136$	0.583683	0.0500504
$137$	−11.0893	−0.947420	−0.473710	−	0.880681i	$-0.657085\pi$
$137$	−11.0893	−0.947420	−0.473710	+	0.880681i	$0.657085\pi$
$138$	0	0
$139$	−4.19223	−0.355581	−0.177790	−	0.984068i	$-0.556895\pi$
$139$	−4.19223	−0.355581	−0.177790	+	0.984068i	$0.556895\pi$
$140$	0.557477	0.0471154
$141$	3.12156	0.262883
$142$	−2.92096	−0.245121
$143$	−20.6877	−1.72999
$144$	−2.92472	−0.243726
$145$	2.12655	0.176600
$146$	−7.94647	−0.657654
$147$	1.83536	0.151378
$148$	9.86429	0.810840
$149$	−9.54267	−0.781766	−0.390883	−	0.920440i	$-0.627830\pi$
$149$	−9.54267	−0.781766	−0.390883	+	0.920440i	$0.627830\pi$
$150$	0.274376	0.0224027
$151$	−9.62412	−0.783199	−0.391600	−	0.920136i	$-0.628078\pi$
$151$	−9.62412	−0.783199	−0.391600	+	0.920136i	$0.628078\pi$
$152$	0.242239	0.0196482
$153$	1.70711	0.138011
$154$	−2.82686	−0.227795
$155$	−2.36730	−0.190146
$156$	1.11939	0.0896228
$157$	10.1179	0.807499	0.403750	−	0.914869i	$-0.367707\pi$
$157$	10.1179	0.807499	0.403750	+	0.914869i	$0.367707\pi$
$158$	−13.7473	−1.09368
$159$	0.455908	0.0361559
$160$	−1.00000	−0.0790569
$161$	0	0
$162$	−8.32813	−0.654320
$163$	−18.3589	−1.43798	−0.718991	−	0.695019i	$-0.755396\pi$
$163$	−18.3589	−1.43798	−0.718991	+	0.695019i	$0.755396\pi$
$164$	−0.782659	−0.0611154
$165$	−1.39131	−0.108313
$166$	−3.81224	−0.295887
$167$	14.6991	1.13745	0.568724	−	0.822528i	$-0.307437\pi$
$167$	14.6991	1.13745	0.568724	+	0.822528i	$0.307437\pi$
$168$	0.152958	0.0118010
$169$	3.64444	0.280342
$170$	0.583683	0.0447664
$171$	0.708481	0.0541789
$172$	3.32343	0.253409
$173$	−1.00476	−0.0763908	−0.0381954	−	0.999270i	$-0.512161\pi$
$173$	−1.00476	−0.0763908	−0.0381954	+	0.999270i	$0.512161\pi$
$174$	0.583475	0.0442331
$175$	0.557477	0.0421413
$176$	5.07081	0.382227
$177$	0.514583	0.0386784
$178$	−15.5397	−1.16475
$179$	2.16190	0.161588	0.0807938	−	0.996731i	$-0.474254\pi$
$179$	2.16190	0.161588	0.0807938	+	0.996731i	$0.474254\pi$
$180$	−2.92472	−0.217996
$181$	19.8940	1.47871	0.739354	−	0.673317i	$-0.235131\pi$
$181$	19.8940	1.47871	0.739354	+	0.673317i	$0.235131\pi$
$182$	2.27437	0.168588
$183$	−3.66809	−0.271153
$184$	0	0
$185$	9.86429	0.725237
$186$	−0.649529	−0.0476258
$187$	−2.95975	−0.216438
$188$	−11.3769	−0.829749
$189$	0.906234	0.0659189
$190$	0.242239	0.0175739
$191$	19.2473	1.39268	0.696341	−	0.717711i	$-0.254810\pi$
$191$	19.2473	1.39268	0.696341	+	0.717711i	$0.254810\pi$
$192$	−0.274376	−0.0198014
$193$	14.2377	1.02486	0.512428	−	0.858730i	$-0.328746\pi$
$193$	14.2377	1.02486	0.512428	+	0.858730i	$0.328746\pi$
$194$	8.24519	0.591970
$195$	1.11939	0.0801611
$196$	−6.68922	−0.477801
$197$	−22.8211	−1.62594	−0.812969	−	0.582308i	$-0.802150\pi$
$197$	−22.8211	−1.62594	−0.812969	+	0.582308i	$0.802150\pi$
$198$	14.8307	1.05397
$199$	−1.19162	−0.0844714	−0.0422357	−	0.999108i	$-0.513448\pi$
$199$	−1.19162	−0.0844714	−0.0422357	+	0.999108i	$0.513448\pi$
$200$	−1.00000	−0.0707107
$201$	1.69588	0.119618
$202$	−9.47663	−0.666774
$203$	1.18550	0.0832060
$204$	0.160149	0.0112126
$205$	−0.782659	−0.0546633
$206$	−9.38768	−0.654070
$207$	0	0
$208$	−4.07976	−0.282880
$209$	−1.22835	−0.0849667
$210$	0.152958	0.0105551
$211$	20.9270	1.44068	0.720338	−	0.693623i	$-0.243987\pi$
$211$	20.9270	1.44068	0.720338	+	0.693623i	$0.243987\pi$
$212$	−1.66162	−0.114120
$213$	−0.801440	−0.0549138
$214$	15.0177	1.02659
$215$	3.32343	0.226656
$216$	−1.62560	−0.110608
$217$	−1.31971	−0.0895879
$218$	13.1767	0.892441
$219$	−2.18032	−0.147332
$220$	5.07081	0.341874
$221$	2.38129	0.160183
$222$	2.70653	0.181650
$223$	22.0139	1.47416	0.737078	−	0.675807i	$-0.236205\pi$
$223$	22.0139	1.47416	0.737078	+	0.675807i	$0.236205\pi$
$224$	−0.557477	−0.0372480
$225$	−2.92472	−0.194981
$226$	−6.95642	−0.462734
$227$	−3.70411	−0.245851	−0.122925	−	0.992416i	$-0.539228\pi$
$227$	−3.70411	−0.245851	−0.122925	+	0.992416i	$0.539228\pi$
$228$	0.0664646	0.00440172
$229$	−24.1493	−1.59583	−0.797914	−	0.602771i	$-0.794063\pi$
$229$	−24.1493	−1.59583	−0.797914	+	0.602771i	$0.794063\pi$
$230$	0	0
$231$	−0.775623	−0.0510322
$232$	−2.12655	−0.139615
$233$	18.1327	1.18791	0.593955	−	0.804498i	$-0.297566\pi$
$233$	18.1327	1.18791	0.593955	+	0.804498i	$0.297566\pi$
$234$	−11.9321	−0.780029
$235$	−11.3769	−0.742150
$236$	−1.87547	−0.122083
$237$	−3.77193	−0.245013
$238$	0.325390	0.0210919
$239$	19.2240	1.24350	0.621750	−	0.783216i	$-0.286422\pi$
$239$	19.2240	1.24350	0.621750	+	0.783216i	$0.286422\pi$
$240$	−0.274376	−0.0177109
$241$	27.0495	1.74241	0.871207	−	0.490916i	$-0.163338\pi$
$241$	27.0495	1.74241	0.871207	+	0.490916i	$0.163338\pi$
$242$	−14.7132	−0.945797
$243$	−7.16184	−0.459432
$244$	13.3689	0.855854
$245$	−6.68922	−0.427359
$246$	−0.214743	−0.0136915
$247$	0.988277	0.0628826
$248$	2.36730	0.150323
$249$	−1.04599	−0.0662867
$250$	−1.00000	−0.0632456
$251$	−12.3635	−0.780380	−0.390190	−	0.920734i	$-0.627591\pi$
$251$	−12.3635	−0.780380	−0.390190	+	0.920734i	$0.627591\pi$
$252$	−1.63046	−0.102709
$253$	0	0
$254$	−10.0296	−0.629314
$255$	0.160149	0.0100289
$256$	1.00000	0.0625000
$257$	−0.194689	−0.0121443	−0.00607217	−	0.999982i	$-0.501933\pi$
$257$	−0.194689	−0.0121443	−0.00607217	+	0.999982i	$0.501933\pi$
$258$	0.911870	0.0567705
$259$	5.49911	0.341698
$260$	−4.07976	−0.253016
$261$	−6.21956	−0.384981
$262$	−16.5560	−1.02283
$263$	−6.15452	−0.379504	−0.189752	−	0.981832i	$-0.560768\pi$
$263$	−6.15452	−0.379504	−0.189752	+	0.981832i	$0.560768\pi$
$264$	1.39131	0.0856292
$265$	−1.66162	−0.102072
$266$	0.135043	0.00827999
$267$	−4.26372	−0.260935
$268$	−6.18087	−0.377556
$269$	15.2470	0.929628	0.464814	−	0.885408i	$-0.346121\pi$
$269$	15.2470	0.929628	0.464814	+	0.885408i	$0.346121\pi$
$270$	−1.62560	−0.0989309
$271$	−26.9300	−1.63588	−0.817940	−	0.575304i	$-0.804884\pi$
$271$	−26.9300	−1.63588	−0.817940	+	0.575304i	$0.804884\pi$
$272$	−0.583683	−0.0353910
$273$	0.624033	0.0377682
$274$	11.0893	0.669927
$275$	5.07081	0.305782
$276$	0	0
$277$	4.57420	0.274837	0.137419	−	0.990513i	$-0.456119\pi$
$277$	4.57420	0.274837	0.137419	+	0.990513i	$0.456119\pi$
$278$	4.19223	0.251433
$279$	6.92367	0.414509
$280$	−0.557477	−0.0333156
$281$	7.34008	0.437873	0.218936	−	0.975739i	$-0.429741\pi$
$281$	7.34008	0.437873	0.218936	+	0.975739i	$0.429741\pi$
$282$	−3.12156	−0.185886
$283$	−3.23302	−0.192183	−0.0960915	−	0.995373i	$-0.530634\pi$
$283$	−3.23302	−0.192183	−0.0960915	+	0.995373i	$0.530634\pi$
$284$	2.92096	0.173327
$285$	0.0664646	0.00393702
$286$	20.6877	1.22329
$287$	−0.436314	−0.0257548
$288$	2.92472	0.172341
$289$	−16.6593	−0.979960
$290$	−2.12655	−0.124875
$291$	2.26228	0.132617
$292$	7.94647	0.465032
$293$	−6.76076	−0.394968	−0.197484	−	0.980306i	$-0.563277\pi$
$293$	−6.76076	−0.394968	−0.197484	+	0.980306i	$0.563277\pi$
$294$	−1.83536	−0.107040
$295$	−1.87547	−0.109194
$296$	−9.86429	−0.573350
$297$	8.24312	0.478314
$298$	9.54267	0.552792
$299$	0	0
$300$	−0.274376	−0.0158411
$301$	1.85274	0.106790
$302$	9.62412	0.553806
$303$	−2.60016	−0.149375
$304$	−0.242239	−0.0138934
$305$	13.3689	0.765499
$306$	−1.70711	−0.0975889
$307$	−9.58018	−0.546770	−0.273385	−	0.961905i	$-0.588143\pi$
$307$	−9.58018	−0.546770	−0.273385	+	0.961905i	$0.588143\pi$
$308$	2.82686	0.161075
$309$	−2.57575	−0.146529
$310$	2.36730	0.134453
$311$	−11.9571	−0.678023	−0.339012	−	0.940782i	$-0.610093\pi$
$311$	−11.9571	−0.678023	−0.339012	+	0.940782i	$0.610093\pi$
$312$	−1.11939	−0.0633729
$313$	−6.25723	−0.353679	−0.176840	−	0.984240i	$-0.556587\pi$
$313$	−6.25723	−0.353679	−0.176840	+	0.984240i	$0.556587\pi$
$314$	−10.1179	−0.570988
$315$	−1.63046	−0.0918661
$316$	13.7473	0.773346
$317$	25.0894	1.40916	0.704582	−	0.709623i	$-0.251135\pi$
$317$	25.0894	1.40916	0.704582	+	0.709623i	$0.251135\pi$
$318$	−0.455908	−0.0255661
$319$	10.7833	0.603751
$320$	1.00000	0.0559017
$321$	4.12049	0.229984
$322$	0	0
$323$	0.141391	0.00786719
$324$	8.32813	0.462674
$325$	−4.07976	−0.226304
$326$	18.3589	1.01681
$327$	3.61538	0.199931
$328$	0.782659	0.0432151
$329$	−6.34238	−0.349667
$330$	1.39131	0.0765891
$331$	−1.72141	−0.0946173	−0.0473087	−	0.998880i	$-0.515064\pi$
$331$	−1.72141	−0.0946173	−0.0473087	+	0.998880i	$0.515064\pi$
$332$	3.81224	0.209224
$333$	−28.8503	−1.58099
$334$	−14.6991	−0.804297
$335$	−6.18087	−0.337697
$336$	−0.152958	−0.00834456
$337$	8.97532	0.488917	0.244458	−	0.969660i	$-0.421390\pi$
$337$	8.97532	0.488917	0.244458	+	0.969660i	$0.421390\pi$
$338$	−3.64444	−0.198232
$339$	−1.90868	−0.103665
$340$	−0.583683	−0.0316547
$341$	−12.0041	−0.650059
$342$	−0.708481	−0.0383102
$343$	−7.63142	−0.412058
$344$	−3.32343	−0.179187
$345$	0	0
$346$	1.00476	0.0540165
$347$	33.0132	1.77224	0.886122	−	0.463452i	$-0.153390\pi$
$347$	33.0132	1.77224	0.886122	+	0.463452i	$0.153390\pi$
$348$	−0.583475	−0.0312775
$349$	−3.86916	−0.207111	−0.103556	−	0.994624i	$-0.533022\pi$
$349$	−3.86916	−0.207111	−0.103556	+	0.994624i	$0.533022\pi$
$350$	−0.557477	−0.0297984
$351$	−6.63206	−0.353993
$352$	−5.07081	−0.270275
$353$	19.8627	1.05719	0.528593	−	0.848875i	$-0.322720\pi$
$353$	19.8627	1.05719	0.528593	+	0.848875i	$0.322720\pi$
$354$	−0.514583	−0.0273498
$355$	2.92096	0.155028
$356$	15.5397	0.823602
$357$	0.0892791	0.00472515
$358$	−2.16190	−0.114260
$359$	−4.61021	−0.243318	−0.121659	−	0.992572i	$-0.538821\pi$
$359$	−4.61021	−0.243318	−0.121659	+	0.992572i	$0.538821\pi$
$360$	2.92472	0.154146
$361$	−18.9413	−0.996912
$362$	−19.8940	−1.04560
$363$	−4.03694	−0.211884
$364$	−2.27437	−0.119209
$365$	7.94647	0.415937
$366$	3.66809	0.191734
$367$	14.0677	0.734326	0.367163	−	0.930157i	$-0.380329\pi$
$367$	14.0677	0.734326	0.367163	+	0.930157i	$0.380329\pi$
$368$	0	0
$369$	2.28906	0.119164
$370$	−9.86429	−0.512820
$371$	−0.926314	−0.0480918
$372$	0.649529	0.0336765
$373$	−6.39186	−0.330958	−0.165479	−	0.986213i	$-0.552917\pi$
$373$	−6.39186	−0.330958	−0.165479	+	0.986213i	$0.552917\pi$
$374$	2.95975	0.153045
$375$	−0.274376	−0.0141687
$376$	11.3769	0.586721
$377$	−8.67582	−0.446827
$378$	−0.906234	−0.0466117
$379$	−4.41056	−0.226555	−0.113278	−	0.993563i	$-0.536135\pi$
$379$	−4.41056	−0.226555	−0.113278	+	0.993563i	$0.536135\pi$
$380$	−0.242239	−0.0124266
$381$	−2.75189	−0.140983
$382$	−19.2473	−0.984775
$383$	−23.7313	−1.21261	−0.606307	−	0.795230i	$-0.707350\pi$
$383$	−23.7313	−1.21261	−0.606307	+	0.795230i	$0.707350\pi$
$384$	0.274376	0.0140017
$385$	2.82686	0.144070
$386$	−14.2377	−0.724682
$387$	−9.72010	−0.494100
$388$	−8.24519	−0.418586
$389$	2.10758	0.106859	0.0534294	−	0.998572i	$-0.482985\pi$
$389$	2.10758	0.106859	0.0534294	+	0.998572i	$0.482985\pi$
$390$	−1.11939	−0.0566824
$391$	0	0
$392$	6.68922	0.337857
$393$	−4.54256	−0.229142
$394$	22.8211	1.14971
$395$	13.7473	0.691701
$396$	−14.8307	−0.745271
$397$	18.7725	0.942167	0.471083	−	0.882089i	$-0.343863\pi$
$397$	18.7725	0.942167	0.471083	+	0.882089i	$0.343863\pi$
$398$	1.19162	0.0597303
$399$	0.0370525	0.00185494
$400$	1.00000	0.0500000
$401$	37.5706	1.87619	0.938093	−	0.346383i	$-0.112590\pi$
$401$	37.5706	1.87619	0.938093	+	0.346383i	$0.112590\pi$
$402$	−1.69588	−0.0845829
$403$	9.65800	0.481099
$404$	9.47663	0.471480
$405$	8.32813	0.413828
$406$	−1.18550	−0.0588355
$407$	50.0200	2.47940
$408$	−0.160149	−0.00792854
$409$	−17.3097	−0.855911	−0.427955	−	0.903800i	$-0.640766\pi$
$409$	−17.3097	−0.855911	−0.427955	+	0.903800i	$0.640766\pi$
$410$	0.782659	0.0386528
$411$	3.04263	0.150082
$412$	9.38768	0.462498
$413$	−1.04553	−0.0514471
$414$	0	0
$415$	3.81224	0.187135
$416$	4.07976	0.200027
$417$	1.15025	0.0563279
$418$	1.22835	0.0600805
$419$	29.9963	1.46542	0.732708	−	0.680543i	$-0.238256\pi$
$419$	29.9963	1.46542	0.732708	+	0.680543i	$0.238256\pi$
$420$	−0.152958	−0.00746360
$421$	−1.96236	−0.0956396	−0.0478198	−	0.998856i	$-0.515227\pi$
$421$	−1.96236	−0.0956396	−0.0478198	+	0.998856i	$0.515227\pi$
$422$	−20.9270	−1.01871
$423$	33.2744	1.61785
$424$	1.66162	0.0806954
$425$	−0.583683	−0.0283128
$426$	0.801440	0.0388299
$427$	7.45283	0.360668
$428$	−15.0177	−0.725907
$429$	5.67621	0.274050
$430$	−3.32343	−0.160270
$431$	13.6167	0.655892	0.327946	−	0.944697i	$-0.393644\pi$
$431$	13.6167	0.655892	0.327946	+	0.944697i	$0.393644\pi$
$432$	1.62560	0.0782117
$433$	−26.1278	−1.25562	−0.627810	−	0.778367i	$-0.716048\pi$
$433$	−26.1278	−1.25562	−0.627810	+	0.778367i	$0.716048\pi$
$434$	1.31971	0.0633482
$435$	−0.583475	−0.0279755
$436$	−13.1767	−0.631051
$437$	0	0
$438$	2.18032	0.104180
$439$	24.4908	1.16888	0.584440	−	0.811437i	$-0.301314\pi$
$439$	24.4908	1.16888	0.584440	+	0.811437i	$0.301314\pi$
$440$	−5.07081	−0.241742
$441$	19.5641	0.931623
$442$	−2.38129	−0.113266
$443$	4.22551	0.200760	0.100380	−	0.994949i	$-0.467994\pi$
$443$	4.22551	0.200760	0.100380	+	0.994949i	$0.467994\pi$
$444$	−2.70653	−0.128446
$445$	15.5397	0.736652
$446$	−22.0139	−1.04239
$447$	2.61828	0.123840
$448$	0.557477	0.0263383
$449$	26.7048	1.26028	0.630138	−	0.776483i	$-0.282998\pi$
$449$	26.7048	1.26028	0.630138	+	0.776483i	$0.282998\pi$
$450$	2.92472	0.137873
$451$	−3.96872	−0.186880
$452$	6.95642	0.327203
$453$	2.64063	0.124067
$454$	3.70411	0.173843
$455$	−2.27437	−0.106624
$456$	−0.0664646	−0.00311249
$457$	20.4598	0.957070	0.478535	−	0.878068i	$-0.341168\pi$
$457$	20.4598	0.957070	0.478535	+	0.878068i	$0.341168\pi$
$458$	24.1493	1.12842
$459$	−0.948835	−0.0442878
$460$	0	0
$461$	−39.8465	−1.85584	−0.927918	−	0.372783i	$-0.878404\pi$
$461$	−39.8465	−1.85584	−0.927918	+	0.372783i	$0.878404\pi$
$462$	0.775623	0.0360852
$463$	−14.8021	−0.687910	−0.343955	−	0.938986i	$-0.611767\pi$
$463$	−14.8021	−0.687910	−0.343955	+	0.938986i	$0.611767\pi$
$464$	2.12655	0.0987227
$465$	0.649529	0.0301212
$466$	−18.1327	−0.839979
$467$	11.5958	0.536589	0.268294	−	0.963337i	$-0.413540\pi$
$467$	11.5958	0.536589	0.268294	+	0.963337i	$0.413540\pi$
$468$	11.9321	0.551564
$469$	−3.44569	−0.159107
$470$	11.3769	0.524779
$471$	−2.77612	−0.127917
$472$	1.87547	0.0863254
$473$	16.8525	0.774879
$474$	3.77193	0.173250
$475$	−0.242239	−0.0111147
$476$	−0.325390	−0.0149142
$477$	4.85977	0.222513
$478$	−19.2240	−0.879287
$479$	31.8196	1.45387	0.726937	−	0.686705i	$-0.240943\pi$
$479$	31.8196	1.45387	0.726937	+	0.686705i	$0.240943\pi$
$480$	0.274376	0.0125235
$481$	−40.2440	−1.83497
$482$	−27.0495	−1.23207
$483$	0	0
$484$	14.7132	0.668780
$485$	−8.24519	−0.374395
$486$	7.16184	0.324868
$487$	−37.5857	−1.70317	−0.851586	−	0.524215i	$-0.824359\pi$
$487$	−37.5857	−1.70317	−0.851586	+	0.524215i	$0.824359\pi$
$488$	−13.3689	−0.605180
$489$	5.03725	0.227792
$490$	6.68922	0.302188
$491$	39.1924	1.76873	0.884364	−	0.466797i	$-0.154592\pi$
$491$	39.1924	1.76873	0.884364	+	0.466797i	$0.154592\pi$
$492$	0.214743	0.00968136
$493$	−1.24123	−0.0559023
$494$	−0.988277	−0.0444647
$495$	−14.8307	−0.666590
$496$	−2.36730	−0.106295
$497$	1.62837	0.0730422
$498$	1.04599	0.0468718
$499$	0.104379	0.00467265	0.00233632	−	0.999997i	$-0.499256\pi$
$499$	0.104379	0.00467265	0.00233632	+	0.999997i	$0.499256\pi$
$500$	1.00000	0.0447214
$501$	−4.03307	−0.180184
$502$	12.3635	0.551812
$503$	13.2502	0.590795	0.295398	−	0.955374i	$-0.404548\pi$
$503$	13.2502	0.590795	0.295398	+	0.955374i	$0.404548\pi$
$504$	1.63046	0.0726266
$505$	9.47663	0.421705
$506$	0	0
$507$	−0.999948	−0.0444092
$508$	10.0296	0.444992
$509$	12.6039	0.558657	0.279329	−	0.960196i	$-0.409888\pi$
$509$	12.6039	0.558657	0.279329	+	0.960196i	$0.409888\pi$
$510$	−0.160149	−0.00709150
$511$	4.42997	0.195970
$512$	−1.00000	−0.0441942
$513$	−0.393784	−0.0173860
$514$	0.194689	0.00858734
$515$	9.38768	0.413670
$516$	−0.911870	−0.0401428
$517$	−57.6904	−2.53722
$518$	−5.49911	−0.241617
$519$	0.275683	0.0121012
$520$	4.07976	0.178909
$521$	14.4493	0.633036	0.316518	−	0.948586i	$-0.397486\pi$
$521$	14.4493	0.633036	0.316518	+	0.948586i	$0.397486\pi$
$522$	6.21956	0.272223
$523$	−30.4865	−1.33308	−0.666541	−	0.745468i	$-0.732226\pi$
$523$	−30.4865	−1.33308	−0.666541	+	0.745468i	$0.732226\pi$
$524$	16.5560	0.723250
$525$	−0.152958	−0.00667564
$526$	6.15452	0.268350
$527$	1.38175	0.0601900
$528$	−1.39131	−0.0605490
$529$	0	0
$530$	1.66162	0.0721761
$531$	5.48521	0.238038
$532$	−0.135043	−0.00585484
$533$	3.19306	0.138307
$534$	4.26372	0.184509
$535$	−15.0177	−0.649271
$536$	6.18087	0.266973
$537$	−0.593172	−0.0255973
$538$	−15.2470	−0.657346
$539$	−33.9198	−1.46103
$540$	1.62560	0.0699547
$541$	26.5111	1.13980	0.569901	−	0.821713i	$-0.306981\pi$
$541$	26.5111	1.13980	0.569901	+	0.821713i	$0.306981\pi$
$542$	26.9300	1.15674
$543$	−5.45843	−0.234244
$544$	0.583683	0.0250252
$545$	−13.1767	−0.564429
$546$	−0.624033	−0.0267061
$547$	32.5161	1.39029	0.695143	−	0.718871i	$-0.255341\pi$
$547$	32.5161	1.39029	0.695143	+	0.718871i	$0.255341\pi$
$548$	−11.0893	−0.473710
$549$	−39.1001	−1.66875
$550$	−5.07081	−0.216220
$551$	−0.515134	−0.0219454
$552$	0	0
$553$	7.66380	0.325898
$554$	−4.57420	−0.194339
$555$	−2.70653	−0.114886
$556$	−4.19223	−0.177790
$557$	20.9562	0.887943	0.443972	−	0.896041i	$-0.353569\pi$
$557$	20.9562	0.887943	0.443972	+	0.896041i	$0.353569\pi$
$558$	−6.92367	−0.293102
$559$	−13.5588	−0.573476
$560$	0.557477	0.0235577
$561$	0.812084	0.0342862
$562$	−7.34008	−0.309623
$563$	10.8713	0.458171	0.229086	−	0.973406i	$-0.426426\pi$
$563$	10.8713	0.458171	0.229086	+	0.973406i	$0.426426\pi$
$564$	3.12156	0.131441
$565$	6.95642	0.292659
$566$	3.23302	0.135894
$567$	4.64274	0.194977
$568$	−2.92096	−0.122561
$569$	24.5362	1.02861	0.514305	−	0.857608i	$-0.328050\pi$
$569$	24.5362	1.02861	0.514305	+	0.857608i	$0.328050\pi$
$570$	−0.0664646	−0.00278389
$571$	35.6465	1.49176	0.745880	−	0.666081i	$-0.232029\pi$
$571$	35.6465	1.49176	0.745880	+	0.666081i	$0.232029\pi$
$572$	−20.6877	−0.864996
$573$	−5.28099	−0.220616
$574$	0.436314	0.0182114
$575$	0	0
$576$	−2.92472	−0.121863
$577$	5.26755	0.219291	0.109646	−	0.993971i	$-0.465028\pi$
$577$	5.26755	0.219291	0.109646	+	0.993971i	$0.465028\pi$
$578$	16.6593	0.692936
$579$	−3.90650	−0.162348
$580$	2.12655	0.0883002
$581$	2.12524	0.0881696
$582$	−2.26228	−0.0937746
$583$	−8.42576	−0.348959
$584$	−7.94647	−0.328827
$585$	11.9321	0.493334
$586$	6.76076	0.279285
$587$	22.1509	0.914266	0.457133	−	0.889398i	$-0.348876\pi$
$587$	22.1509	0.914266	0.457133	+	0.889398i	$0.348876\pi$
$588$	1.83536	0.0756890
$589$	0.573451	0.0236286
$590$	1.87547	0.0772118
$591$	6.26157	0.257566
$592$	9.86429	0.405420
$593$	−11.2091	−0.460302	−0.230151	−	0.973155i	$-0.573922\pi$
$593$	−11.2091	−0.460302	−0.230151	+	0.973155i	$0.573922\pi$
$594$	−8.24312	−0.338219
$595$	−0.325390	−0.0133397
$596$	−9.54267	−0.390883
$597$	0.326951	0.0133812
$598$	0	0
$599$	36.0050	1.47112	0.735562	−	0.677457i	$-0.236918\pi$
$599$	36.0050	1.47112	0.735562	+	0.677457i	$0.236918\pi$
$600$	0.274376	0.0112014
$601$	−38.8131	−1.58322	−0.791610	−	0.611027i	$-0.790757\pi$
$601$	−38.8131	−1.58322	−0.791610	+	0.611027i	$0.790757\pi$
$602$	−1.85274	−0.0755119
$603$	18.0773	0.736164
$604$	−9.62412	−0.391600
$605$	14.7132	0.598175
$606$	2.60016	0.105624
$607$	−26.0184	−1.05605	−0.528027	−	0.849227i	$-0.677068\pi$
$607$	−26.0184	−1.05605	−0.528027	+	0.849227i	$0.677068\pi$
$608$	0.242239	0.00982409
$609$	−0.325274	−0.0131807
$610$	−13.3689	−0.541289
$611$	46.4152	1.87776
$612$	1.70711	0.0690057
$613$	−16.7945	−0.678323	−0.339161	−	0.940728i	$-0.610143\pi$
$613$	−16.7945	−0.678323	−0.339161	+	0.940728i	$0.610143\pi$
$614$	9.58018	0.386625
$615$	0.214743	0.00865927
$616$	−2.82686	−0.113897
$617$	18.9635	0.763441	0.381720	−	0.924278i	$-0.375332\pi$
$617$	18.9635	0.763441	0.381720	+	0.924278i	$0.375332\pi$
$618$	2.57575	0.103612
$619$	−4.93612	−0.198399	−0.0991997	−	0.995068i	$-0.531628\pi$
$619$	−4.93612	−0.198399	−0.0991997	+	0.995068i	$0.531628\pi$
$620$	−2.36730	−0.0950729
$621$	0	0
$622$	11.9571	0.479435
$623$	8.66301	0.347076
$624$	1.11939	0.0448114
$625$	1.00000	0.0400000
$626$	6.25723	0.250089
$627$	0.337029	0.0134597
$628$	10.1179	0.403750
$629$	−5.75762	−0.229571
$630$	1.63046	0.0649592
$631$	37.8899	1.50837	0.754187	−	0.656660i	$-0.228031\pi$
$631$	37.8899	1.50837	0.754187	+	0.656660i	$0.228031\pi$
$632$	−13.7473	−0.546838
$633$	−5.74187	−0.228219
$634$	−25.0894	−0.996429
$635$	10.0296	0.398013
$636$	0.455908	0.0180779
$637$	27.2904	1.08129
$638$	−10.7833	−0.426917
$639$	−8.54297	−0.337955
$640$	−1.00000	−0.0395285
$641$	4.23414	0.167239	0.0836193	−	0.996498i	$-0.473352\pi$
$641$	4.23414	0.167239	0.0836193	+	0.996498i	$0.473352\pi$
$642$	−4.12049	−0.162623
$643$	7.49055	0.295398	0.147699	−	0.989032i	$-0.452813\pi$
$643$	7.49055	0.295398	0.147699	+	0.989032i	$0.452813\pi$
$644$	0	0
$645$	−0.911870	−0.0359048
$646$	−0.141391	−0.00556295
$647$	28.1031	1.10485	0.552423	−	0.833564i	$-0.313703\pi$
$647$	28.1031	1.10485	0.552423	+	0.833564i	$0.313703\pi$
$648$	−8.32813	−0.327160
$649$	−9.51015	−0.373306
$650$	4.07976	0.160021
$651$	0.362097	0.0141917
$652$	−18.3589	−0.718991
$653$	−28.6699	−1.12194	−0.560970	−	0.827836i	$-0.689572\pi$
$653$	−28.6699	−1.12194	−0.560970	+	0.827836i	$0.689572\pi$
$654$	−3.61538	−0.141373
$655$	16.5560	0.646895
$656$	−0.782659	−0.0305577
$657$	−23.2412	−0.906725
$658$	6.34238	0.247252
$659$	−7.05851	−0.274960	−0.137480	−	0.990505i	$-0.543900\pi$
$659$	−7.05851	−0.274960	−0.137480	+	0.990505i	$0.543900\pi$
$660$	−1.39131	−0.0541567
$661$	26.6714	1.03740	0.518699	−	0.854957i	$-0.326417\pi$
$661$	26.6714	1.03740	0.518699	+	0.854957i	$0.326417\pi$
$662$	1.72141	0.0669046
$663$	−0.653368	−0.0253747
$664$	−3.81224	−0.147944
$665$	−0.135043	−0.00523673
$666$	28.8503	1.11793
$667$	0	0
$668$	14.6991	0.568724
$669$	−6.04007	−0.233523
$670$	6.18087	0.238788
$671$	67.7910	2.61704
$672$	0.152958	0.00590049
$673$	9.66359	0.372504	0.186252	−	0.982502i	$-0.440366\pi$
$673$	9.66359	0.372504	0.186252	+	0.982502i	$0.440366\pi$
$674$	−8.97532	−0.345716
$675$	1.62560	0.0625694
$676$	3.64444	0.140171
$677$	−37.6633	−1.44752	−0.723759	−	0.690053i	$-0.757587\pi$
$677$	−37.6633	−1.44752	−0.723759	+	0.690053i	$0.757587\pi$
$678$	1.90868	0.0733022
$679$	−4.59650	−0.176397
$680$	0.583683	0.0223832
$681$	1.01632	0.0389455
$682$	12.0041	0.459661
$683$	−46.4586	−1.77769	−0.888844	−	0.458209i	$-0.848491\pi$
$683$	−46.4586	−1.77769	−0.888844	+	0.458209i	$0.848491\pi$
$684$	0.708481	0.0270894
$685$	−11.0893	−0.423699
$686$	7.63142	0.291369
$687$	6.62598	0.252797
$688$	3.32343	0.126705
$689$	6.77901	0.258260
$690$	0	0
$691$	51.7450	1.96847	0.984237	−	0.176856i	$-0.0565927\pi$
$691$	51.7450	1.96847	0.984237	+	0.176856i	$0.0565927\pi$
$692$	−1.00476	−0.0381954
$693$	−8.26777	−0.314067
$694$	−33.0132	−1.25317
$695$	−4.19223	−0.159020
$696$	0.583475	0.0221165
$697$	0.456825	0.0173035
$698$	3.86916	0.146450
$699$	−4.97517	−0.188178
$700$	0.557477	0.0210706
$701$	37.1189	1.40196	0.700981	−	0.713180i	$-0.252746\pi$
$701$	37.1189	1.40196	0.700981	+	0.713180i	$0.252746\pi$
$702$	6.63206	0.250311
$703$	−2.38952	−0.0901223
$704$	5.07081	0.191113
$705$	3.12156	0.117565
$706$	−19.8627	−0.747544
$707$	5.28300	0.198688
$708$	0.514583	0.0193392
$709$	25.6270	0.962442	0.481221	−	0.876599i	$-0.340194\pi$
$709$	25.6270	0.962442	0.481221	+	0.876599i	$0.340194\pi$
$710$	−2.92096	−0.109622
$711$	−40.2070	−1.50788
$712$	−15.5397	−0.582374
$713$	0	0
$714$	−0.0892791	−0.00334119
$715$	−20.6877	−0.773676
$716$	2.16190	0.0807938
$717$	−5.27461	−0.196984
$718$	4.61021	0.172052
$719$	32.4967	1.21192	0.605961	−	0.795495i	$-0.292789\pi$
$719$	32.4967	1.21192	0.605961	+	0.795495i	$0.292789\pi$
$720$	−2.92472	−0.108998
$721$	5.23341	0.194902
$722$	18.9413	0.704923
$723$	−7.42175	−0.276018
$724$	19.8940	0.739354
$725$	2.12655	0.0789781
$726$	4.03694	0.149825
$727$	3.24205	0.120241	0.0601206	−	0.998191i	$-0.480851\pi$
$727$	3.24205	0.120241	0.0601206	+	0.998191i	$0.480851\pi$
$728$	2.27437	0.0842938
$729$	−23.0193	−0.852568
$730$	−7.94647	−0.294112
$731$	−1.93983	−0.0717472
$732$	−3.66809	−0.135577
$733$	−48.9596	−1.80836	−0.904182	−	0.427147i	$-0.859519\pi$
$733$	−48.9596	−1.80836	−0.904182	+	0.427147i	$0.859519\pi$
$734$	−14.0677	−0.519247
$735$	1.83536	0.0676983
$736$	0	0
$737$	−31.3420	−1.15450
$738$	−2.28906	−0.0842614
$739$	5.63647	0.207341	0.103671	−	0.994612i	$-0.466941\pi$
$739$	5.63647	0.207341	0.103671	+	0.994612i	$0.466941\pi$
$740$	9.86429	0.362619
$741$	−0.271159	−0.00996129
$742$	0.926314	0.0340061
$743$	−22.2662	−0.816867	−0.408433	−	0.912788i	$-0.633925\pi$
$743$	−22.2662	−0.816867	−0.408433	+	0.912788i	$0.633925\pi$
$744$	−0.649529	−0.0238129
$745$	−9.54267	−0.349617
$746$	6.39186	0.234023
$747$	−11.1497	−0.407947
$748$	−2.95975	−0.108219
$749$	−8.37201	−0.305907
$750$	0.274376	0.0100188
$751$	18.2585	0.666263	0.333132	−	0.942880i	$-0.391895\pi$
$751$	18.2585	0.666263	0.333132	+	0.942880i	$0.391895\pi$
$752$	−11.3769	−0.414875
$753$	3.39226	0.123621
$754$	8.67582	0.315955
$755$	−9.62412	−0.350257
$756$	0.906234	0.0329594
$757$	13.1146	0.476657	0.238329	−	0.971185i	$-0.423401\pi$
$757$	13.1146	0.476657	0.238329	+	0.971185i	$0.423401\pi$
$758$	4.41056	0.160199
$759$	0	0
$760$	0.242239	0.00878693
$761$	−30.5373	−1.10698	−0.553489	−	0.832857i	$-0.686704\pi$
$761$	−30.5373	−1.10698	−0.553489	+	0.832857i	$0.686704\pi$
$762$	2.75189	0.0996903
$763$	−7.34572	−0.265933
$764$	19.2473	0.696341
$765$	1.70711	0.0617206
$766$	23.7313	0.857448
$767$	7.65146	0.276278
$768$	−0.274376	−0.00990069
$769$	−28.3915	−1.02382	−0.511912	−	0.859038i	$-0.671062\pi$
$769$	−28.3915	−1.02382	−0.511912	+	0.859038i	$0.671062\pi$
$770$	−2.82686	−0.101873
$771$	0.0534179	0.00192380
$772$	14.2377	0.512428
$773$	−29.0840	−1.04608	−0.523040	−	0.852308i	$-0.675202\pi$
$773$	−29.0840	−1.04608	−0.523040	+	0.852308i	$0.675202\pi$
$774$	9.72010	0.349382
$775$	−2.36730	−0.0850358
$776$	8.24519	0.295985
$777$	−1.50883	−0.0541288
$778$	−2.10758	−0.0755605
$779$	0.189591	0.00679279
$780$	1.11939	0.0400805
$781$	14.8116	0.530002
$782$	0	0
$783$	3.45692	0.123540
$784$	−6.68922	−0.238901
$785$	10.1179	0.361125
$786$	4.54256	0.162028
$787$	45.0279	1.60507	0.802536	−	0.596604i	$-0.203484\pi$
$787$	45.0279	1.60507	0.802536	+	0.596604i	$0.203484\pi$
$788$	−22.8211	−0.812969
$789$	1.68865	0.0601176
$790$	−13.7473	−0.489107
$791$	3.87804	0.137887
$792$	14.8307	0.526986
$793$	−54.5417	−1.93683
$794$	−18.7725	−0.666213
$795$	0.455908	0.0161694
$796$	−1.19162	−0.0422357
$797$	−37.9031	−1.34260	−0.671299	−	0.741187i	$-0.734263\pi$
$797$	−37.9031	−1.34260	−0.671299	+	0.741187i	$0.734263\pi$
$798$	−0.0370525	−0.00131164
$799$	6.64053	0.234925
$800$	−1.00000	−0.0353553
$801$	−45.4492	−1.60587
$802$	−37.5706	−1.32666
$803$	40.2951	1.42198
$804$	1.69588	0.0598091
$805$	0	0
$806$	−9.65800	−0.340188
$807$	−4.18342	−0.147263
$808$	−9.47663	−0.333387
$809$	44.8456	1.57669	0.788343	−	0.615236i	$-0.210939\pi$
$809$	44.8456	1.57669	0.788343	+	0.615236i	$0.210939\pi$
$810$	−8.32813	−0.292621
$811$	−7.92686	−0.278350	−0.139175	−	0.990268i	$-0.544445\pi$
$811$	−7.92686	−0.278350	−0.139175	+	0.990268i	$0.544445\pi$
$812$	1.18550	0.0416030
$813$	7.38894	0.259141
$814$	−50.0200	−1.75320
$815$	−18.3589	−0.643086
$816$	0.160149	0.00560632
$817$	−0.805065	−0.0281657
$818$	17.3097	0.605220
$819$	6.65190	0.232436
$820$	−0.782659	−0.0273316
$821$	−44.8858	−1.56652	−0.783262	−	0.621691i	$-0.786446\pi$
$821$	−44.8858	−1.56652	−0.783262	+	0.621691i	$0.786446\pi$
$822$	−3.04263	−0.106124
$823$	40.8346	1.42340	0.711702	−	0.702481i	$-0.247925\pi$
$823$	40.8346	1.42340	0.711702	+	0.702481i	$0.247925\pi$
$824$	−9.38768	−0.327035
$825$	−1.39131	−0.0484392
$826$	1.04553	0.0363786
$827$	19.7597	0.687112	0.343556	−	0.939132i	$-0.388369\pi$
$827$	19.7597	0.687112	0.343556	+	0.939132i	$0.388369\pi$
$828$	0	0
$829$	−37.8794	−1.31561	−0.657803	−	0.753190i	$-0.728514\pi$
$829$	−37.8794	−1.31561	−0.657803	+	0.753190i	$0.728514\pi$
$830$	−3.81224	−0.132325
$831$	−1.25505	−0.0435372
$832$	−4.07976	−0.141440
$833$	3.90438	0.135279
$834$	−1.15025	−0.0398298
$835$	14.6991	0.508682
$836$	−1.22835	−0.0424833
$837$	−3.84828	−0.133016
$838$	−29.9963	−1.03621
$839$	−30.1267	−1.04009	−0.520045	−	0.854139i	$-0.674085\pi$
$839$	−30.1267	−1.04009	−0.520045	+	0.854139i	$0.674085\pi$
$840$	0.152958	0.00527756
$841$	−24.4778	−0.844061
$842$	1.96236	0.0676274
$843$	−2.01394	−0.0693638
$844$	20.9270	0.720338
$845$	3.64444	0.125373
$846$	−33.2744	−1.14400
$847$	8.20224	0.281832
$848$	−1.66162	−0.0570602
$849$	0.887062	0.0304439
$850$	0.583683	0.0200202
$851$	0	0
$852$	−0.801440	−0.0274569
$853$	−31.2512	−1.07002	−0.535011	−	0.844845i	$-0.679693\pi$
$853$	−31.2512	−1.07002	−0.535011	+	0.844845i	$0.679693\pi$
$854$	−7.45283	−0.255031
$855$	0.708481	0.0242295
$856$	15.0177	0.513294
$857$	−53.5902	−1.83061	−0.915303	−	0.402767i	$-0.868049\pi$
$857$	−53.5902	−1.83061	−0.915303	+	0.402767i	$0.868049\pi$
$858$	−5.67621	−0.193783
$859$	−23.6993	−0.808610	−0.404305	−	0.914624i	$-0.632487\pi$
$859$	−23.6993	−0.808610	−0.404305	+	0.914624i	$0.632487\pi$
$860$	3.32343	0.113328
$861$	0.119714	0.00407985
$862$	−13.6167	−0.463785
$863$	−32.7071	−1.11336	−0.556680	−	0.830727i	$-0.687925\pi$
$863$	−32.7071	−1.11336	−0.556680	+	0.830727i	$0.687925\pi$
$864$	−1.62560	−0.0553040
$865$	−1.00476	−0.0341630
$866$	26.1278	0.887857
$867$	4.57092	0.155236
$868$	−1.31971	−0.0447939
$869$	69.7100	2.36475
$870$	0.583475	0.0197816
$871$	25.2164	0.854427
$872$	13.1767	0.446221
$873$	24.1148	0.816164
$874$	0	0
$875$	0.557477	0.0188462
$876$	−2.18032	−0.0736662
$877$	−17.6102	−0.594654	−0.297327	−	0.954776i	$-0.596095\pi$
$877$	−17.6102	−0.594654	−0.297327	+	0.954776i	$0.596095\pi$
$878$	−24.4908	−0.826524
$879$	1.85499	0.0625673
$880$	5.07081	0.170937
$881$	28.6272	0.964476	0.482238	−	0.876040i	$-0.339824\pi$
$881$	28.6272	0.964476	0.482238	+	0.876040i	$0.339824\pi$
$882$	−19.5641	−0.658757
$883$	51.0592	1.71828	0.859139	−	0.511742i	$-0.170999\pi$
$883$	51.0592	1.71828	0.859139	+	0.511742i	$0.170999\pi$
$884$	2.38129	0.0800913
$885$	0.514583	0.0172975
$886$	−4.22551	−0.141959
$887$	12.0579	0.404865	0.202433	−	0.979296i	$-0.435115\pi$
$887$	12.0579	0.404865	0.202433	+	0.979296i	$0.435115\pi$
$888$	2.70653	0.0908250
$889$	5.59128	0.187526
$890$	−15.5397	−0.520891
$891$	42.2304	1.41477
$892$	22.0139	0.737078
$893$	2.75594	0.0922240
$894$	−2.61828	−0.0875684
$895$	2.16190	0.0722642
$896$	−0.557477	−0.0186240
$897$	0	0
$898$	−26.7048	−0.891149
$899$	−5.03417	−0.167899
$900$	−2.92472	−0.0974906
$901$	0.969859	0.0323107
$902$	3.96872	0.132144
$903$	−0.508346	−0.0169167
$904$	−6.95642	−0.231367
$905$	19.8940	0.661298
$906$	−2.64063	−0.0877289
$907$	−54.9116	−1.82331	−0.911656	−	0.410955i	$-0.865195\pi$
$907$	−54.9116	−1.82331	−0.911656	+	0.410955i	$0.865195\pi$
$908$	−3.70411	−0.122925
$909$	−27.7165	−0.919298
$910$	2.27437	0.0753947
$911$	−15.0735	−0.499408	−0.249704	−	0.968322i	$-0.580333\pi$
$911$	−15.0735	−0.499408	−0.249704	+	0.968322i	$0.580333\pi$
$912$	0.0664646	0.00220086
$913$	19.3312	0.639768
$914$	−20.4598	−0.676751
$915$	−3.66809	−0.121263
$916$	−24.1493	−0.797914
$917$	9.22956	0.304787
$918$	0.948835	0.0313162
$919$	−23.0078	−0.758958	−0.379479	−	0.925200i	$-0.623897\pi$
$919$	−23.0078	−0.758958	−0.379479	+	0.925200i	$0.623897\pi$
$920$	0	0
$921$	2.62857	0.0866144
$922$	39.8465	1.31227
$923$	−11.9168	−0.392246
$924$	−0.775623	−0.0255161
$925$	9.86429	0.324336
$926$	14.8021	0.486426
$927$	−27.4563	−0.901783
$928$	−2.12655	−0.0698075
$929$	34.9190	1.14566	0.572828	−	0.819676i	$-0.305846\pi$
$929$	34.9190	1.14566	0.572828	+	0.819676i	$0.305846\pi$
$930$	−0.649529	−0.0212989
$931$	1.62039	0.0531061
$932$	18.1327	0.593955
$933$	3.28073	0.107406
$934$	−11.5958	−0.379426
$935$	−2.95975	−0.0967941
$936$	−11.9321	−0.390014
$937$	15.4899	0.506034	0.253017	−	0.967462i	$-0.418577\pi$
$937$	15.4899	0.506034	0.253017	+	0.967462i	$0.418577\pi$
$938$	3.44569	0.112506
$939$	1.71683	0.0560267
$940$	−11.3769	−0.371075
$941$	27.3144	0.890425	0.445213	−	0.895425i	$-0.353128\pi$
$941$	27.3144	0.890425	0.445213	+	0.895425i	$0.353128\pi$
$942$	2.77612	0.0904509
$943$	0	0
$944$	−1.87547	−0.0610413
$945$	0.906234	0.0294798
$946$	−16.8525	−0.547922
$947$	−5.33867	−0.173484	−0.0867418	−	0.996231i	$-0.527646\pi$
$947$	−5.33867	−0.173484	−0.0867418	+	0.996231i	$0.527646\pi$
$948$	−3.77193	−0.122506
$949$	−32.4197	−1.05239
$950$	0.242239	0.00785927
$951$	−6.88394	−0.223227
$952$	0.325390	0.0105459
$953$	−7.54131	−0.244287	−0.122143	−	0.992512i	$-0.538977\pi$
$953$	−7.54131	−0.244287	−0.122143	+	0.992512i	$0.538977\pi$
$954$	−4.85977	−0.157341
$955$	19.2473	0.622827
$956$	19.2240	0.621750
$957$	−2.95869	−0.0956409
$958$	−31.8196	−1.02804
$959$	−6.18201	−0.199627
$960$	−0.274376	−0.00885545
$961$	−25.3959	−0.819223
$962$	40.2440	1.29752
$963$	43.9225	1.41538
$964$	27.0495	0.871207
$965$	14.2377	0.458329
$966$	0	0
$967$	1.49888	0.0482008	0.0241004	−	0.999710i	$-0.492328\pi$
$967$	1.49888	0.0482008	0.0241004	+	0.999710i	$0.492328\pi$
$968$	−14.7132	−0.472899
$969$	−0.0387942	−0.00124625
$970$	8.24519	0.264737
$971$	−1.65676	−0.0531678	−0.0265839	−	0.999647i	$-0.508463\pi$
$971$	−1.65676	−0.0531678	−0.0265839	+	0.999647i	$0.508463\pi$
$972$	−7.16184	−0.229716
$973$	−2.33707	−0.0749231
$974$	37.5857	1.20432
$975$	1.11939	0.0358491
$976$	13.3689	0.427927
$977$	−7.62311	−0.243885	−0.121943	−	0.992537i	$-0.538912\pi$
$977$	−7.62311	−0.243885	−0.121943	+	0.992537i	$0.538912\pi$
$978$	−5.03725	−0.161074
$979$	78.7988	2.51842
$980$	−6.68922	−0.213679
$981$	38.5382	1.23043
$982$	−39.1924	−1.25068
$983$	−35.2843	−1.12540	−0.562698	−	0.826663i	$-0.690237\pi$
$983$	−35.2843	−1.12540	−0.562698	+	0.826663i	$0.690237\pi$
$984$	−0.214743	−0.00684575
$985$	−22.8211	−0.727141
$986$	1.24123	0.0395289
$987$	1.74020	0.0553911
$988$	0.988277	0.0314413
$989$	0	0
$990$	14.8307	0.471351
$991$	1.43911	0.0457147	0.0228573	−	0.999739i	$-0.492724\pi$
$991$	1.43911	0.0457147	0.0228573	+	0.999739i	$0.492724\pi$
$992$	2.36730	0.0751617
$993$	0.472314	0.0149884
$994$	−1.62837	−0.0516486
$995$	−1.19162	−0.0377768
$996$	−1.04599	−0.0331434
$997$	−5.23053	−0.165653	−0.0828263	−	0.996564i	$-0.526395\pi$
$997$	−5.23053	−0.165653	−0.0828263	+	0.996564i	$0.526395\pi$
$998$	−0.104379	−0.00330406
$999$	16.0354	0.507338

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5290.2.a.bj.1.4		10
23.9	even	11		230.2.g.b.81.2	yes	20
23.18	even	11		230.2.g.b.71.2	✓	20
23.22	odd	2		5290.2.a.bi.1.4		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.g.b.71.2	✓	20	23.18	even	11
230.2.g.b.81.2	yes	20	23.9	even	11
5290.2.a.bi.1.4		10	23.22	odd	2
5290.2.a.bj.1.4		10	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 5290 = 2 \cdot 5 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5290.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.274376 q^{3} +1.00000 q^{4} +1.00000 q^{5} +0.274376 q^{6} +0.557477 q^{7} -1.00000 q^{8} -2.92472 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -0.274376 q^{3} +1.00000 q^{4} +1.00000 q^{5} +0.274376 q^{6} +0.557477 q^{7} -1.00000 q^{8} -2.92472 q^{9} -1.00000 q^{10} +5.07081 q^{11} -0.274376 q^{12} -4.07976 q^{13} -0.557477 q^{14} -0.274376 q^{15} +1.00000 q^{16} -0.583683 q^{17} +2.92472 q^{18} -0.242239 q^{19} +1.00000 q^{20} -0.152958 q^{21} -5.07081 q^{22} +0.274376 q^{24} +1.00000 q^{25} +4.07976 q^{26} +1.62560 q^{27} +0.557477 q^{28} +2.12655 q^{29} +0.274376 q^{30} -2.36730 q^{31} -1.00000 q^{32} -1.39131 q^{33} +0.583683 q^{34} +0.557477 q^{35} -2.92472 q^{36} +9.86429 q^{37} +0.242239 q^{38} +1.11939 q^{39} -1.00000 q^{40} -0.782659 q^{41} +0.152958 q^{42} +3.32343 q^{43} +5.07081 q^{44} -2.92472 q^{45} -11.3769 q^{47} -0.274376 q^{48} -6.68922 q^{49} -1.00000 q^{50} +0.160149 q^{51} -4.07976 q^{52} -1.66162 q^{53} -1.62560 q^{54} +5.07081 q^{55} -0.557477 q^{56} +0.0664646 q^{57} -2.12655 q^{58} -1.87547 q^{59} -0.274376 q^{60} +13.3689 q^{61} +2.36730 q^{62} -1.63046 q^{63} +1.00000 q^{64} -4.07976 q^{65} +1.39131 q^{66} -6.18087 q^{67} -0.583683 q^{68} -0.557477 q^{70} +2.92096 q^{71} +2.92472 q^{72} +7.94647 q^{73} -9.86429 q^{74} -0.274376 q^{75} -0.242239 q^{76} +2.82686 q^{77} -1.11939 q^{78} +13.7473 q^{79} +1.00000 q^{80} +8.32813 q^{81} +0.782659 q^{82} +3.81224 q^{83} -0.152958 q^{84} -0.583683 q^{85} -3.32343 q^{86} -0.583475 q^{87} -5.07081 q^{88} +15.5397 q^{89} +2.92472 q^{90} -2.27437 q^{91} +0.649529 q^{93} +11.3769 q^{94} -0.242239 q^{95} +0.274376 q^{96} -8.24519 q^{97} +6.68922 q^{98} -14.8307 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 10 q^{2} + 4 q^{3} + 10 q^{4} + 10 q^{5} - 4 q^{6} - 7 q^{7} - 10 q^{8} + 14 q^{9}+O(q^{10}) \) 10 * q - 10 * q^2 + 4 * q^3 + 10 * q^4 + 10 * q^5 - 4 * q^6 - 7 * q^7 - 10 * q^8 + 14 * q^9	\( 10 q - 10 q^{2} + 4 q^{3} + 10 q^{4} + 10 q^{5} - 4 q^{6} - 7 q^{7} - 10 q^{8} + 14 q^{9} - 10 q^{10} + 9 q^{11} + 4 q^{12} - 7 q^{13} + 7 q^{14} + 4 q^{15} + 10 q^{16} - 18 q^{17} - 14 q^{18} + 16 q^{19} + 10 q^{20} + 12 q^{21} - 9 q^{22} - 4 q^{24} + 10 q^{25} + 7 q^{26} + 13 q^{27} - 7 q^{28} + 10 q^{29} - 4 q^{30} - 3 q^{31} - 10 q^{32} + 25 q^{33} + 18 q^{34} - 7 q^{35} + 14 q^{36} - 8 q^{37} - 16 q^{38} + 12 q^{39} - 10 q^{40} + 10 q^{41} - 12 q^{42} - 9 q^{43} + 9 q^{44} + 14 q^{45} + 21 q^{47} + 4 q^{48} + 7 q^{49} - 10 q^{50} - 9 q^{51} - 7 q^{52} - 40 q^{53} - 13 q^{54} + 9 q^{55} + 7 q^{56} + 9 q^{57} - 10 q^{58} + 29 q^{59} + 4 q^{60} + 25 q^{61} + 3 q^{62} + 6 q^{63} + 10 q^{64} - 7 q^{65} - 25 q^{66} - 7 q^{67} - 18 q^{68} + 7 q^{70} + 64 q^{71} - 14 q^{72} - 16 q^{73} + 8 q^{74} + 4 q^{75} + 16 q^{76} + 57 q^{77} - 12 q^{78} + 44 q^{79} + 10 q^{80} + 14 q^{81} - 10 q^{82} - 26 q^{83} + 12 q^{84} - 18 q^{85} + 9 q^{86} + 25 q^{87} - 9 q^{88} + 11 q^{89} - 14 q^{90} + 5 q^{93} - 21 q^{94} + 16 q^{95} - 4 q^{96} - 10 q^{97} - 7 q^{98} + 13 q^{99}+O(q^{100}) \) 10 * q - 10 * q^2 + 4 * q^3 + 10 * q^4 + 10 * q^5 - 4 * q^6 - 7 * q^7 - 10 * q^8 + 14 * q^9 - 10 * q^10 + 9 * q^11 + 4 * q^12 - 7 * q^13 + 7 * q^14 + 4 * q^15 + 10 * q^16 - 18 * q^17 - 14 * q^18 + 16 * q^19 + 10 * q^20 + 12 * q^21 - 9 * q^22 - 4 * q^24 + 10 * q^25 + 7 * q^26 + 13 * q^27 - 7 * q^28 + 10 * q^29 - 4 * q^30 - 3 * q^31 - 10 * q^32 + 25 * q^33 + 18 * q^34 - 7 * q^35 + 14 * q^36 - 8 * q^37 - 16 * q^38 + 12 * q^39 - 10 * q^40 + 10 * q^41 - 12 * q^42 - 9 * q^43 + 9 * q^44 + 14 * q^45 + 21 * q^47 + 4 * q^48 + 7 * q^49 - 10 * q^50 - 9 * q^51 - 7 * q^52 - 40 * q^53 - 13 * q^54 + 9 * q^55 + 7 * q^56 + 9 * q^57 - 10 * q^58 + 29 * q^59 + 4 * q^60 + 25 * q^61 + 3 * q^62 + 6 * q^63 + 10 * q^64 - 7 * q^65 - 25 * q^66 - 7 * q^67 - 18 * q^68 + 7 * q^70 + 64 * q^71 - 14 * q^72 - 16 * q^73 + 8 * q^74 + 4 * q^75 + 16 * q^76 + 57 * q^77 - 12 * q^78 + 44 * q^79 + 10 * q^80 + 14 * q^81 - 10 * q^82 - 26 * q^83 + 12 * q^84 - 18 * q^85 + 9 * q^86 + 25 * q^87 - 9 * q^88 + 11 * q^89 - 14 * q^90 + 5 * q^93 - 21 * q^94 + 16 * q^95 - 4 * q^96 - 10 * q^97 - 7 * q^98 + 13 * q^99

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